The talks are expected to be held between Pashinyan and acting prime minister Karen Karapetyan.
Mr Sargsyan, who led the country for a decade as president, was confirmed as prime minister last Tuesday, reversing his promise not to take the post.
Pashinyan, who was arrested yesterday and released today shortly after Sargsyan's resignation, returned to Republic Square, the epicenter of nearly two weeks of protest rallies, to thunderous ovation and applause by the thousands gather there.
"I hope that the high echelons of the (ruling) Republican Party will unequivocally recognise the popular velvet and non-violent revolution", he said to loud applause from the crowd. The prime minister walked out after Pashinian made it clear he would only discuss Sargsyan's resignation.
In a surprise announcement posted on his website, Mr Sargsyan said he should not have resisted the opposition's demands.
Pressure on the 63-year-old to quit had increased sharply on Monday when unarmed soldiers in the capital Yerevan joined the anti-government protests, which first erupted on April 13.
Yerevan residents celebrate Armenian Prime Minister's Serzh Sargsyan's resignation in Yerevan, Armenia, April 23, 2018.
The new government system effectively tightened Sargsyan's grip over the country in the South Caucasus.
Armenia's political parties in parliament now have seven days to put forward the name of a new prime minister.
Pashinyan delivered a speech following his release from custody, in which he stated that a new prime minister should be appointed in a week's time.
Pashinian told a rally in Armenia's capital, Yerevan, on Monday evening the opposition will be pushing for a snap parliamentary election and wants to prevent former President Serzh Sargsyan from running the country behind the scenes. Pashinyan reiterated the demand for resignation, and Sargsyan threatened a possible repetition of the March 1, 2008, events, when the army was engaged to disperse the protesters after a contested election, killing ten people.
Writing on Facebook, Pashinyan congratulated the people for the resignation: "You have won, proud citizens of the Republic of Armenia". The quicker they recognize this fact, the better it will be for Armenia and Artsakh.
Sargsyan resigned on Monday following 10 days of massive anti-government protests.
"This regime that was based on fear of people to speak out and protest, is coming to an end", said Gevorg Ter-Gabrielyan, an analyst with the Yerevan-based Eurasia Partnership Foundation, which is supported in part by the United States Agency for International Development (USAID).